Question

A swarm of 62 bees flies in a garden. If 3 bees land on each flower, 8 bees are left with no flowers. Find the number of flowers in a garden.

Answer 1

Hint: Let us assume the total number of bees as x and total number of flowers as y. In the question, we were given that if 3 bees land on each flower, 8 bees are left with no flowers. So, we will find a relation between x and y. In the question, it was already given that the number of bees in a swarm is 62. So, we will get the value of x as 62. By this value of x, we can get the value of y.

Complete step by step solution:
In the question, we were given that if 3 bees land on each flower, 8 bees are left with no flowers.
Let us assume the number of bees as x.
Let us assume the number of flowers as y.
Number of bees on each flower =3.
Number of bees on y flowers =3y.
Number of bees are left =8.
So, the total number of bees \[=3y+8\]
\[\Rightarrow x=3y+8....(1)\]
In the question, we were already given that there are a swarm of 62 bees.
So, from equation (1) we get
\[\begin{align}
  & \Rightarrow 3y+8=62 \\
 & \Rightarrow 3y=54 \\
 & \Rightarrow y=18....(2) \\
\end{align}\]
From equation (2), we get
The total number of flowers are equal to 18.

Note: Some students may have a misconception that if 8 bees are left then the total number of bees are equal to 3y-8. If this procedure is followed, we get
\[\begin{align}
  & \Rightarrow 3y-8=62 \\
 & \Rightarrow 3y=70 \\
 & \Rightarrow y=\dfrac{70}{3} \\
\end{align}\]
So, we get the number of flowers equal to \[\dfrac{70}{3}\]. As \[\dfrac{70}{3}\] is a fraction, it is not possible to take it as the number of flowers. We know that the number of flowers must be an integer. This type of small misconception gives a wrong result.